the perimeter of right angle triangle is 40 cm and its hypotenuse is 2 cm longer than one side find the length of the other side
Answers
We know that if a,b,c are the sides of triangle, then perimeter is a + b + c.
Given that perimeter of a right angled triangle = 40cm.
= > a + b + c = 40
= > b = 40 - a - c ---- (1)
Given that length of its hypotenuse is 2 cm longer than one side.
= > c = a + 2 ---- (2)
By Pythagoras theorem,
= > c^2 = a^2 + b^2 ---- (3)
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Substitute (2) in (1), we get
= > b = 40 - a - c
= > b = 40 - a - (a + 2)
= > b = 40 - a - a - 2
= > b = 38 - 2a ------- (4)
Substitute (2),(4) in (3), we get
= > c^2 = a^2 + (38 - 2a)^2
= > (a + 2)^2 = a^2 + 1444 + 4a^2 - 152a
= > a^2 + 4 + 4a = 5a^2 - 152a + 1444
= > a^2 + 156a - 1440 = 5a^2
= > -4a^2 + 156a - 1440 = 0
= > a^2 - 39a + 360 = 0
= > a^2 - 24a - 15a + 360 = 0
= > a(a - 24) - 15(a - 24) = 0
= > (a - 24)(a - 15) = 0
= > a = 24, b = 15.
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Now,
When a = 24:
= > b = 38 - 2(24)
= 38 - 48
= -10. (cannot be negative).
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When a = 15:
Then,
= > b = 38 - 2(15)
= 38 - 30
= 8.
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= > c^2 = a^2 + b^2
= 15^2 + 8^2
= 225 + 64
= 289
= > c = 17cm.
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Therefore, the length of other sides are 15cm,8cm, 17cm.
Hope this helps!
Hope it helps uh :)
